Research On Optimal Control-Based Trajectory Planning Methods For Computer Numerical Control Systems

Numerical control(NC)machines are important equipment of the machinery manufacturing industry,and play a major role in the domestic economy and national defense.With an increasing demand for both accuracy and productivity of the machining processes,the traditional NC trajectory planning strategy becomes powerless.Hence it is necessary to design more reasonable trajectory planning strategy to fully utilize the maximum ability of machines and further increase the productivity and decrease machining wear of the process.In this thesis,based on the optimal control theory and methods,efficient trajectory planning methods of computer numerical control(CNC)systems are studied.In the thesis,a series of numerical methods for solving optimal control problems with path constraints are studied systematically based on control vector parameterization.These methods include the linear mapping and nonlinear mapping approaches for handling free time,the KS function based and Sigmoid function based constraint-aggregation approaches for solving the path constraints,a multi-stage optimization strategy for problem with switch structure,and a Lagrangian multiplier algorithm for constrained optimization problems.Examples are solved to demonstrate the effectiveness of the given methods.Further,based on these given methods,the optimal trajectory planning problems for CNC systems are studied in detail.On the issue of planning time optimal trajectory for CNC system under given path,the optimal control formula of the problem is constructed and a series of properties of the optimal trajectory are proven,such as the bang-bang accelerate and decelerate structure of time optimal trajectory.Control trajectory parameterization and state trajectory parameterization methods are proposed to realize the numerical solution of the trajectory optimization problems.An equivalence property of time optimal trajectory and velocity maximum trajectory is proven.And an efficient numerical method based on linear programming is proposed to obtain the time optimal trajectory,which implies the optimized solution can be obtained in polynomial time complexity.Besides,robust time optimal trajectory solution by linear programming method is presented for problem with model uncertainty.However in practical applications,the “bang-bang” acceleration/ deceleration structure of time optimal trajectory can induce tool vibrations,reduce the machining precision and shorten the machine life.To solve these problems,more practical smooth time optimal trajectory planning methods are studied in this thesis to realize the continuous acceleration/deceleration structure.According to the optimal control theory,the constraints structure of smooth time optimal trajectory is proven to be “bang-bang”,and an efficient smooth trajectory planning method based on convex programming is proposed.The effectiveness of the proposed method is demonstrated by an impeller trajectory planning on five-axis machine and a serial manipulator trajectory tracking problem.The point by point machining processes,such as drilling,spot welding/scanning and assembly et al,are widespread in manufacturing industry.The machining process of these problems does not have decided path,even the machining order of these points is also unknown.This thesis presents mix integer optimal control formulas for these problems.Specially,a decoupling strategy is proposed to solve the point by point machining problems with start-stop operations.The strategy is implemented by solving a series of point to point motion planning problems and a master combinatorial optimization problem.And a nested optimization strategy is proposed to realize the solution of the point by point machining problems without start-stop operations.The details of this nested strategy include solutions of minimum time trajectory planning problem under spline interpolation path in the inner loop and a solution of combinatorial optimization problem in the outer loop.